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arXiv:2307.11372math.PR

On the origin of the Boltzmann distribution

Fedor Sandomirskiy, Omer Tamuz

Abstract

The family of Boltzmann distributions is used in statistical mechanics to describe the distribution of states in systems with a given temperature. We give a novel characterization of this family as the unique one satisfying independence for uncoupled systems. The theorem boils down to a statement about endomorphisms of the convolution semi-group of finitely supported probability measures on the natural numbers, or, alternatively, about endomorphisms of the multiplicative semi-group of polynomials with non-negative coefficients.

arXiv comments
Journal reference
DOI
Subjects
math.PRProbability cond-mat.stat-mechStatistical Mechanics math.GRGroup Theory

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  1. Economics Puzzle Leads to a New Understanding of a Fundamental Law of Physics 1 comment

    • More specifically, dice-inspired (positive integer-related) probability distributions https://arxiv.org/abs/2307.11372 tilt maps [on dice polynomials].. that are measure-class-preserving and commute with convolution. as an alternative to max entropy to derive Boltzmann law for…

      gsf_emergency_6View on HNParent context

  2. A 'crazy' dice proof leads to new understanding of a fundamental law of physics 1 comment

    • Original article: "On the origin of the Boltzmann distribution" - https://arxiv.org/abs/2307.11372 Abstract: "Boltzmann distributions are used in statistical mechanics to describe how the states of a system are distributed at a given temperature. We give a novel characterization…

      bikenagaView on HNParent context

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